This paper investigates cooperative control of a collection of vehicles operating in a vehicular ad hoc network (VANET) with access-constrained fading channels. To establish a systematic methodology, we first formulate and solve the problem for general networked control systems (NCSs) where the sensors communicate with the controller via access-constrained fading channels. By introducing a Markov chain model for the random access protocol of the communication network and modeling the fading for each channel as an independent stochastic process with known probability distribution, we derive a new model of NCSs. Then, based on the new system model, a framework for stability analysis and controller design is developed, which is also extended to a more complicated case in which the transition probabilities of the Markov access protocol are partially unknown. The results are then extended and applied to a platoon of vehicles operating in a VANET. The effectiveness of the obtained method is shown by both numerical simulations and experiments with laboratory-scale Arduino cars.